Experiment 9 - AC Circuits

Experiment 9 - AC Circuits - Eric Chong Partner: Albert Lee...

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Eric Chong PHYS C1493 Partner: Albert Lee Lab Date: November 30, 2006 Experiment 9: AC Circuits Introduction This lab makes widespread use of the digital oscilloscope in efforts to study the time and frequency-dependant behavior of an AC circuit, which is a circuit whose current is driven by a voltage that varies with the passage of time. With the AC circuit containing a resistance R , capacitance C , and inductance L subject to varying frequencies of a sinusoidal voltage V , we relate the voltage across the resistor V R as a function of angular frequency ω to find the resonant frequency and the full width at half maximum FWHM, using calculated graphs. We also use the oscilloscope to gauge the phase difference between the driving voltage and the voltage across the resistor. The experimental values for resonant frequency ω 0 and phase difference φ can then be compared to calculated values, given by the following equations: 0 1 LC ϖ = , 1/ tan L C R φ - = Procedure Resonance We begin this experiment by setting up the RLC circuit such that the inductor, capacitor, and a decade resistor box are connected in series with a function generator and an oscilloscope. Initially the decade resistor box is set to a resistance of 50 Ω using a knob on the function generator, and the function generator set to produce a sinusoidal signal in the range of 1 kHz , with a peak-to-peak voltage of V pp = 20 V . Making sure that CH 2 on the oscilloscope is connected across the resistor, we vary the frequency on the function generator such that the wave displayed on CH 2 peaks at some maximum value – the frequency at this peak value is the resonance frequency, ω 0 . After recording this value, we scan over a wide range of frequencies both above and below ω 0 , taking into record frequencies and their respective peak-to- peak voltages as given by the oscilloscope. We need a wide enough range such that we can find and record the FWHM of the signal – thus we record voltage amplitudes of at least 20 points above and below ω 0 . This procedure is repeated for resistances of 10 Ω and 500 Ω. We then replace the 150 mH inductor in the RLC circuit with a large copper ring of inductance 0.0225 H , and using the function generator to sweep through a variety of frequencies, we use the same method we used earlier to find the resonance frequency ω 0 . Using this value along with the value of C , we can estimate the inductance L of the copper ring using the equation given in the introduction. Phase of Driving Voltage and V R We revert back to the 150 mH inductor and eliminate the copper ring, while setting the resistance to 30 Ω – we should once again be able to see the driving voltage on CH 1 of the oscilloscope
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and the voltage across the resistor on CH 2. In comparing the two sinusoidal curves, we proceed in taking into account the relationship between the two when the frequency on the function generator is varied above and below ω 0 – we do this qualitatively by pointing out which curve
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This note was uploaded on 12/16/2010 for the course PHYS 1493 taught by Professor Lab during the Spring '08 term at Columbia.

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Experiment 9 - AC Circuits - Eric Chong Partner: Albert Lee...

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